低频振动单相不可压缩流体细管流动微观动力学数学模型研究

Mathematical Model of Microscopic Dynamics about Single-Phrase Incompressible Fluid Flows in Thin Tube under Low Frequency Vibration

为揭示低频振动对地层以及流体流动规律的影响,鉴于储层孔隙体系结构的复杂性,采用细管多孔介质模型,针对单一细管中的单相不可压缩流体,将低频波对流体流动产生惯性力引入圆管层流的Naver—Stokes(N—S)方程,建立了低频振动条件下单相不可压缩流体在细管中流动的微观动力学模型。该模型采用C—N差分格式,对低频振动条件下单一细管中流体流速以及剪切力分布进行模拟计算和定量分析。结果表明,低频振动条件下圆管中的流速随管径呈抛物线型分布,随时间以不振动下速度分布为中心轴线呈周期性变化;黏附层处剪切力也是随时间以不振动下的剪切力为中心轴线呈现周期性变化,当剪切力大于黏附层流动的临界剪切力时,黏附层会部分发生流动。该模型的建立与求解,为进一步揭示低频振动对地层渗透性微观动力学增效机制提供了重要认识。

In order to discover the effect of low frequency wave on strata and the law of fluid flow,mathematical model of microscopic dynamics about single-phrase incompressible fluid flows in thin tube under low frequency vibration was established,which is based on inertial force that produced from low frequency vibration when fluid motion is induced into N-S equation of tube with laminar.Using this C-N differential format,fluid velocity and shear force distribution in single thin tube were simulated and quantitatively analyzed under low frequency vibration.The results show that fluid flow rate presents a parabolic distribution with diameter and a periodical change that centered on no-vibration fluid velocity distribution with time in single thin tube under low frequency vibration;shear force at adhesion layer also presents a periodical change that centered on no-vibration fluid velocity distribution with time.When the shear force is greater than the critical shear force of the adhesive layer flows,the portions of the adhesive layer will flow.Establishment and solution of the model provide an important understanding for further discovery of the microscopic dynamics synergistic mechanism that low-frequency vibration has on the formation permeability.